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# Compare Values of Logarithmic Scales

Calculator for the comparison of two values, whose size is measured in a logarithmic scale. At a logarithmic scale, the intensity doesn't grow linear, but exponential, it multiplies with every increment. Often, a decadic logarithm is used, that is to the base 10. If a value is increased by 1 (e.g. from 1 to 2 or from 5 to 6), then the intensity tenfolds. A value of 0 doesn't mean that there is no intensity, but usually, this is very low then, for the decadic logarithm 0 is a tenth of 1.
Please enter three values to calculate a fourth one. For the base can also be entered e for the natural logarithm.

 First value (a): Second value (b): Base of the scale (s): Ratio a to b (r):

Round to    decimal places.

The formulas are: r = sa-b, s = a-b r , a-b = logs(r)

Example: for a natural logarithmic scale (base e=2,718281828459045), the value 6 is a bit more than 20 times as strong as the value 3.

The logarithm is the inverse of the exponential function. The exponential function ax initially increases slightly, but then increases rapidly very quickly. Therefore the logarithm first increases quickly, then very slowly. Logarithmic scales are used when the values that occur have a very wide spread and you also want to record the low and high values without having to deal with many decimal places or with very large numbers. The downside is that the logarithmic scale is not very intuitive; if you don't have experience with it, you tend to greatly underestimate the differences between the values. An earthquake of magnitude 8 is a million times more powerful than one of magnitude 2.
If you want to calculate with logarithmically scaled values, special rules must be applied. E.g. the usual arithmetic mean is not permitted as the mean between two or more values; the geometric mean is used instead.

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German: Logarithmische Skalen

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